If you deposit $5,339 into a fund (today) that earns 6% interest compounded monthly,what minimum payment can you withdraw at the end of each month for 5 years so that the account has a $0 balance.

Question

If you deposit $5,339 into a fund (today) that earns 6% interest compounded monthly,what minimum payment can you withdraw at the end of each month for 5 years so that the account has a $0 balance.  

Answer 1

This is a time value of money question ; specifically Ordinary annuity.

It is basically asking you to find the recurring payments(PMT) given the present value (PV) amount of $5339

Using a financial calculator(I'm using Texas Instrument BA II Plus), input the following;

Present value; PV = -5339

Total duration; N = 5*12 = 60 months

Monthly interest rate ; I = 6%/12 = 0.5%

Future value; FV = 0

then press on CPT PMT = $103.22

Answer 2

The cash Flow structure here is EXACTLY THE SAME as borrowing 5,339 today and making a payment monthly for 5 years. Actually, the Fund is borrowing your money for 5 years .

So We know that PV=Payment*β(i,n) where β is a multiplier you might get from a loan table. It is simply the present value of 1 dollar compounded for n periods at Rate I

β =(1/i)(1-(1/(1+i))^N) nhere i = 6%/12 (compounding Monthly) and n=12*5 = 60 months

sooooooo, β=(1/(6%/12)(1-(1/(1+6%/12))⁶⁰) = 20*(1- (1/(1.005))⁶⁰) = 200*(1-.74137)=200*(.25862)=51.7255

so PV=PMT*5.17255 or PMT = 5339/51.71255 = 103.21 per month

hope this helps